Suppose that in Horsehead, Massachusetts, the cost of operating a lobster boat i

Question

Suppose that in Horsehead, Massachusetts, the cost of operating a lobster boat is $5,000 per month. Suppose that if x lobster boats operate in the bay, the total monthly revenue from lobster boats in the bay is $1,000(21x - x2). If there are no restrictions on entry and new boats come into the bay until there is no profit to be made by a new entrant, then the number of boats who enter will be Xi If the number of boats that operate in the bay is regulated to maximize total profits, the number of boats in the bay will be X2. Xi = 16 and X, = 16. Xi = 20 and X, = 12. Xi = 16 and X, = 8. d. X, = 8 and X, = 6. c. None of the above

Explanation / Answer

Profits = Revenue - Costs= 1000(21x-x2) - 5000x= 16000x-1000x2

X1= no. of boats where profits are zero i.e. 16000X1-1000X12=0 i.e. X1=16

X2= no. of boats where profits are maximum

Therefore, differentiating the profit function w.r.t. x we get: 16000-2000x

For maximum, equating it to zer we get: x=8. Hence, X2=8.

CORRECT OPTION is c.

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